- Code: Select all
`174: Ocean #7/18 (9.9)`

1 2 3 4 5 6 7 8 9

+-------+-------+-------+

a| . . 1 | . . 2 | . . 3 |

b| . 2 . | . 4 . | . 1 . |

c| 5 . . | 6 . . | . . . |

+-------+-------+-------+

d| . . . | . . 7 | . . 1 |

e| . 3 . | . 8 . | . 2 . |

f| 4 . . | 5 . . | 6 . . |

+-------+-------+-------+

g| . . 5 | . . 9 | . . 2 |

h| . 7 . | . . . | . 8 . |

k| 3 . . | . . . | 9 . . |

+-------+-------+-------+

2. h1=1, g7=1, f2=1, h3=9, k3=2, c3=4, d1=2, f5=2, h4=2, f6=3, e1=9, b3=3, c5=3, c6=1, e4=1, k5=1, g4=3, h7=3, d8=3, cf8=79, k9=7, g5=7, k46=8, c8=7, f8=9, f9=8, c9=9, c2=8, a2=9, g1=8, b4=9, d4=4, d7=8, d3=6, e3=7, box6!=7 contradiction > h1!=1

3. e1=1, ghk4=1 or f2=1, g1=1, h7=1 > g5h56!=1

4. f5=2 or f3=2, h1=2 > h5!=2

5. k5=2, (d4=2, f3=2, h1=2, h3=9, e13=7, e46=4, e7=5, e9=9, df5=9, ab7c9=478, c8=9

5a. k3=4 or c3=4, a7=4, d8=4, c2=8, c9=7, f8=7, g7=7, k4=7, b7=8, a4=8, k6=8, k3=6, k8=5, k9=4 > k3!=8, k2468!=4

5b. b4=9, ghk4=3 or b1=9, f2=9, e1=1, e4=4, h6=4, h47=13 > h56!=3, h47=13

5c. h5=5 or a5=5, b9=5 > h9!=5, h56=5

5d. e4=4, h6=4 or e6=4, h56=56 , k6!=6, h6=6 > h6!=5 > h5=5, a5=7, a8=5, k9=5, b9=6, h9=4, a7=4, g4=4, k3=4, k4=7, h6=6, k6=8, d5=6, d3=8, c2=4, c9=8, box6!=8 >) k5!=2, hk4=2, d4!=2

6. f5=2 or d5=2, (f3=2, h1=2, h3=9, k4=2, e13=7, e6=6, de4=4, e3=7

6a. c3=4, (c56=13, c89=7, abe7=458, d7=3, f9=8, f8=7, c8=9, e9=9, e1=1, cf56=13 non-unique contradiction >) k3=4, h6=4, h9k89=567, h47=13, k89=7, ab7=7, c5=7, c6=1, f6=3, g4=7, k6=8, b6=5, a5=9) f5=1 > f5=12

7. k6=1, (f6=3, c6=8, b6=5, c5=1, e4=1, b4=3, c3=3, c89=7, b7=8, f9=8, a45=79, f5=2, bef3=679, h1=9, e13f3=679, c2=9, b9=9, c89=47, h34=24, a8=6, k8=5, h6=6, h9=nil contradiction >) k6!=1

8. d5=3, (f6=1, c5=1, f8=3, gh7=13, a5=9, b6=5, e6=6, e1=1, d48=49, d7=8, b7=7, a4=7, column1!=7 contradiction >) d5!=3

9. f6=3 or d4=3, f6=1, c5=1, bc6=3 > h6!=3

10. g4=3, (h7=3, f6=3, c5=3, d8=3, b3=3, g7=1, k2=1, h4=1, c6=1, f5=1, e1=1, d5=2, f3=2, h1=2, k4=2, h3=9, e3=7, e6=6, k6=8, b6=5, h6=4, a5=9, b19=69, a1=7, b4=7, column7!=7 contradiction >) g4!=3

11. f3=2, (d5=2, h1=2, k4=2, f5=1, k2=1, e1=1, c6=1, f6=3, e6=6, de4=49, h3=9, e3=7

11a. k3=4 or c3=4, c5=3, h4=3, g4=1, k6=8 > k3!=8, k6=8, h6=4, b6=5

11b. b4=3 or b3=3, b47=78, a1=7, a4=8, b4=7 > b4!=8, a4=8

11c. f8=7 or f8=9, f2=8, d7=8, b7=7 > ac8!=7

11d. g4=7 or b4=7, c9=7, f8=7, g7=7 > g58!=7

11e. b7=8, f9=8, f8=7 or b7=7, b4=3, c3=3, k3=4, g12=68, g5=3, g8=4, c8=9, f8=7 > f8=7

11f. b7=7 or b7=8, f9=8, f2=9, ab1=79, a15=79, g7=7, b4=7, c9=7 > a7!=7, b9!=7, ae7=45, h47=13, g47=17, x-wing bg47=7, b1!=7, a1=7, a5=9

11g. c3=4 or k3=4, g8=4 > c8!=4, c8=9, b1=9, f2=9, e9=9, f9=8, d7=3, d8=4, k9=4, a7=4, g2=4, c3=4, h7=1, k3=6, k8=5, box3!=5 contradiction >) f3!=2, f5=2 (the hardest step by far)

12. h7=4, abe7=578, d7=3, f6=3, g7=1, k2=1, row6!=1 > h7!=4

13. c5=3, (b3=3, h4=3, f6=3, h7=1, c6=1, h13=29, k4=2, e4=1, k5=1, f2=1, g1=1, d45=9, g45=7, ac2=9

13a. h5=5 or a5=5, k8=5 > k6!=5, h9!=5

13b. k3=4 or c3=4, c89=7, e7=7, f8=9, f9=8, c2=8, k3=8, g4=8, b6=8, h6=5, k6=4 > k289!=4, k3!=6

13c. h5=6 or h5=5, b6=5, k6=8 > k6!=6, k36=48, k2=6

13d. k3=4 or c3=4, c89=7, e7=7, e9=5, e6=4 > k6!=4, k6=8, k3=4, b6=5, h5=5, g2=8

13e. d4=9, b47=78, b1=6 or d4=4, g4=7, g5=6, h9=6, b1=6 > b1=6, a8=6, h9=6, h6=4, g4=7, d4=4, a5=7, c3=7, e1=7, b7=7, a7=5, e9=5, k8=5, a2=4, c2=9, f8=7, column8!=9 contradiction >) c5!=3, gh5=3, h4!=3

14. k5=1, (c6=1, e4=1, f2=1, g1=1, h7=1, f6=3, b4=3, c3=3, h5=3, a5=5, k8=5, h6=5, b6=8, d45=9, ac2=9, b13=67, b7=5, b9=9, f8=9, a8=6, e9=5, c9=8, f9=7, e7=4, e6=6, k6=4, h4=2, k3=2, d1=2, g5=6, k2=6, d4=4, a7=7, c8=4, h9=4, row8!=6 contradiction >) k5!=1, c5=1, ef6=1, e4!=1

15. e1=1 or e6=1, f2=1, g1=1, h7=1, k4=1, h4=2, k3=2, d1=2, f6=3, h5=3, b4=3, c3=3, c6=8, g4=8, k3=8, b6=5, k5=5, h9=5, a8=5, e7=5, d5=6, a4=7, g5=7, b7=7, box1!=7 contradiction > e1=1, f6=1, d4=3, f8=3ef3=7, c89=7, abd7=458, e7=7, f3=7, e9=5, gh7=13, k8=5

16. g1=6, a2=6, column8!=6 contradiction > g1=8 (very short and elegant),…

or with the same result: 16. g1=6 or g1=8, k6=8, c6=3, b6=5, a7=5, d7=4, d8=9, d5=6, e6=4, h6=6, k5=7, g8=7, g2=6 > g58!=6, a8=6, bf9=89, g12=6, g2=6, k2=1, hk3=4

17. f9=9, d8=4, g8=7 or f2=9, e3=6, d5=6, k5=7, g8=7 > g8=7, etc. trivial.

One could also use a sort of "back door" after step 5:

6. g5=3, (h7=3, g7=1, k2=1, e1=1, h4=1, k4=2, h13=29, ef3=7

6a. f3=2, e3=7 or f5=2, c5=1, c89=7, e7=7, f3=7 > f3=27, e9!=7

6b. k6=8, cf6=13, b6=5 or g4=8, g1=6, a2=6, b9=6, k8=6, a8=5, b6=5 > b6=5, eh6=46, k6=8 (2 numbers solved)

6c. e7=7, b7=8, a4=8 or e3=7, f3=2, f5=1, f6=3, c6=1, ac5=79, a4=8 > a4=8 (1 number solved)

6d. e7=7, b7=8, d7=4 or e3=7, f3=2, f5=1, f6=3, d8=3 > d8!=4

6e. e7=7, b7=8, d7=4, f9=8, f2=9 or e3=7, f3=2, h3=9 > de3!=9

6f. f6=1, f8=3, d8=9 or f5=1, ac5=79 > d5!=9, de4=9, b4!=9

6g. b4=7, g4=4, k3=4 or b4=3, c3=3, k3=4 > k3=4, g12=6, g8!=6, ak8=56 (2 numbers solved)

6h. e7=7, a7=5, a8=6 or a7=7, a5=9, a1=6 > a2!=6, g2=6, g1=8 (2 numbers solved)

6i. f2=9 or f2=8, d7=8, b7=7, a1=7, a5=9 > a2!=9, a2=4, de7=4, e9!=4 (1 number solved)

6j. a7=7, a5=9, a1=6 or e7=7, e3=6 > d1!=6, de3=6, b3!=6, dh1=29, a5=9 (2 numbers solved)

6k. f5=2, f6=1, f8=3 or f5=1, c5=7, g4=7, k9=7, f3=2, f8=7 > f8!=9, f29=89

6l. c2=9, b9=9 or f2=9 > f9!=9, f9=8, f2=9, c2=8, a7=8, d7=4, d1=2, h1=9, h3=2, f3=7, e3=6, d5=6, e6=4, e4=9, e9=5, e7=7, a7=5, a8=6, h6=6, h9=4, g8=7, k8=5, k9=6, h5=5, k5=7, g4=4, c5=1, c6=3, c3=9, b3=3, a1=7, b1=6, b4=7, b9=9, c9=7, c8=4, f8=3, d8=9, d3=8, d4=3, f5=2, f6=1 solution complete, no contradiction >) g5=3 (at last)

Well, I called it "back door" because the remaining steps are rather simple forcing chains. Perhaps there is another "break through"-step in 6a-6k, I didn't see it, so I had to painstakingly solve only one or two numbers at a time.

Thank you again for this wonderful puzzle, Ocean.

Kind regards, Maria